# We now apply the Box-Cox transform using the best parameter lambda found above.
R_, _ = transformation.boxcox_transform(R, metadata, Lambda)
data.append((R_ - np.mean(R_)) / np.std(R_))
labels.append("Box-Cox\n($\lambda=$%.2f)" % Lambda)
skw.append(skew(R_))
###############################################################################
# Normal quantile transform
# ~~~~~~~~~~~~~~~~~~~~~~~~~
# At last, we apply the empirical normal quantile (NQ) transform as described in
# `Bogner et al (2012)`_.
#
# .. _`Bogner et al (2012)`: http://dx.doi.org/10.5194/hess-16-1085-2012
R_, _ = transformation.NQ_transform(R, metadata)
data.append((R_ - np.mean(R_)) / np.std(R_))
labels.append("NQ")
skw.append(skew(R_))
###############################################################################
# By plotting all the results, we can notice first of all the strongly asymmetric
# distribution of the original data (R) and that all transformations manage to
# reduce its skewness. Among these, the Box-Cox transform (using the best parameter
# lambda) and the normal quantile (NQ) transform provide the best correction.
# Despite not producing a perfectly symmetric distribution, the square-root (sqrt)
# transform has the strong advantage of being defined for zeros, too, while all
# other transformations need an arbitrary rule for non-positive values.
plot_distribution(data, labels, skw)
plt.title("Data transforms")
def test_NQ_transform(R, metadata, inverse, expected):
"""Test the NQ_transform."""
assert_array_almost_equal(
transformation.NQ_transform(R, metadata, inverse)[0], expected
)
